Double solutions of unsteady stagnation-point of Carbon Nanotubes across a permeable exponential stretching/shrinking sheet

Abstract

Carbon nanotube (CNTs) has an extraordinary interest due to its escalating applications in industry and technological processes. Thus, the analysis of unsteady stagnation-point of carbon nanotubes through exponential permeable (extending/shrinking) sheet with slip effects is inspected in this work. Comprising SWCNTs/MWCNTs which suspended into a carrier fluid (Water (H2O) or kerosene (oil)). The similarity transformation technique is adapted to attain the dimensionless system of differential equations from the envisioned mathematical model in (pde). Later, the finite difference method is utilized in MATLAB software to attain the approximate solutions. The outcomes of quantities of practical interest versus crucial parameters are discussed graphically and interpreted physically. According to the finding, the double solution discovered for both extending and shrinking, the addition of SWCNTs volume fraction will speed up the separation of flow at the critical point, stability analysis performed the rational of first solution as time evolves. Finally, this analysis supports the adoption of controlling parameters in abroad range of distinct industries including processing and biomedical.